Question

integration of sin^4x cos^4x

Answer 1

Here is your answer...
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Let [text]\displaystyle I = \int \sin^4(x) - \cos^4(x) \, dx[/text]

[text]\displaystyle = \int (\sin^2(x) + \cos^2(x))(\sin^2(x) - \cos^2(x)) \, dx[/text]

[text]\displaystyle = \int \sin^2(x) - \cos^2(x) \, dx[/text] (As, [text]\sin^2(x) + \cos^2(x) = 1[/text])

[text]\displaystyle = \int -\cos(2x) \, dx[/text] (As, [text]\cos^2(x) - \sin^2(x) = \cos(2x)[/text])

[text]\displaystyle = \dfrac{-\sin(2x)}{2} + C[/text] (where [text]C[/text] is the arbitrary constant of indefinite integration)...

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